Dust particles need to grow efficiently from micrometre sizes to thousands of kilometres to form planets. With the growth of millimetre to meter sizes being hindered by a number of barriers, the recent discovery that dust evolution is able to create `self-induced' dust traps shows promises. The condensation and sublimation of volatile species at certain locations, called snow lines, is also thought to be an important part of planet formation scenarios. Given that dust sticking properties change across a snow line, this raises the question: how do snow lines affect the self-induced dust trap formation mechanism? The question is particularly relevant with the multiple observations of the carbon monoxide (CO) snow line in protoplanetary discs, since its effect on dust growth and dynamics is yet to be understood. In this paper, we present the effects of snow lines in general on the formation of self-induced dust traps in a parameter study, then focus on the CO snow line. We find that for a range of parameters, a dust trap forms at the snow line where the dust accumulates and slowly grows, as found for the water snow line in previous work. We also find that, depending on the grains sticking properties on either side of the CO snow line, it could either be a starting or braking point for dust growth and drift. This could provide clues to understand the link between dust distributions and snow lines in protoplanetary disc observations.
CO is thought to be a vital building block for prebiotic molecules that are necessary for life. Thus, understanding where CO existed in a solid phase within the solar nebula is important for understanding the origin of life. We model the evolution of the CO snow line in a protoplanetary disk. We find that the current observed location of the CO snow line in our solar system, and in the solar system analogue TW Hydra, cannot be explained by a fully turbulent disk model. With time-dependent disk models we find that the inclusion of a dead zone (a region of low turbulence) can resolve this proble…
We examine the evolution of the snow line in a protoplanetary disc that contains a dead zone (a region of zero or low turbulence). The snow line is within a self-gravitating part of the dead zone, and we obtain a fully analytic solution for its radius. Our formula could prove useful for future observational attempts to characterise the demographics of planets outside the snow line. External sources such as comic rays or X-rays from the central star can ionise the disc surface layers and allow the magneto-rotational instability to drive turbulence there. We show that provided that the surface d…
We model the evolution of the snow line in a protoplanetary disc. If the magneto-rotational instability (MRI) drives turbulence throughout the disc, there is a unique snow line outside of which the disc is icy. The snow line moves closer to the star as the infall accretion rate drops. Because the snow line moves inside the radius of the Earth's orbit, the formation of our water-devoid planet is difficult with this model. However, protoplanetary discs are not likely to be sufficiently ionised to be fully turbulent. A dead zone at the mid-plane slows the flow of material through the disc and a s…
The water snowline in protoplanetary disks is one of the most pivotal locations for planet formation: it sets a critical boundary of chemical composition in the disk and likely serves as a favorable site of planetesimal growth and planet formation. However, the water snowline at the mid-plane cannot be directly traced by water line observations as the dust emission around the water snowline is highly optically thick at these line frequencies. Alternatively, the water snowline maybe traced through the sharp changes in physical properties (surface density and dust size distribution) at this tran…
Aims. We track the time evolution of planet traps and snowlines in a viscously evolving protoplanetary disk using an opacity table that accounts for the composition of the dust material. Methods. We coupled a dynamical and thermodynamical disk model with a temperature-dependent opacity table (that accounts for the sublimation of the main dust components) to investigate the formation and evolution of snowlines and planet traps during the first million years of disk evolution. Results. Starting from a minimum mass solar nebula (MMSN), we find that the disk mid-plane temperature profile shows sev…
Evolution of a snow line in an optically-thick protoplanetary disk is investigated with numerical simulations. The ice-condensing region in the disk is obtained by calculating the temperature and the density with the 1+1D approach. The snow line migrates as the mass accretion rate (\dot{M}) in the disk decreases with time. Calculations are carried out from an early phase with high disk accretion rates (\dot{M} \sim 10^{-7} M_sun/yr) to a later phase with low disk accretion rates (\dot{M} \sim 10^{-12} M_sun/yr) using the same numerical method. It is found that the snow line moves inward for \d…
The snow line in a protoplanetary disk demarcates regions with H$_2$O ice from regions with H$_2$O vapor. Where a planet forms relative to this location determines how much water and other volatiles it forms with. Giant planet formation may be triggered at the water snow line if vapor diffuses outward and is cold-trapped beyond the snow line faster than icy particles can drift inward. In this study we investigate the distribution of water across the snow line, considering three different radial profiles of the turbulence parameter $α(r)$, corresponding to three different angular momentum trans…
High resolution ALMA observations of protoplanetary disks have revealed that many, if not all primordial disks consist of ring-like dust structures. The origin of these dust rings remains unclear, but a common explanation is the presence of planetary companions that have cleared gaps along their orbit and trapped the dust at the gap edge. A signature of this scenario is a decrease of gas density inside these gaps. In recent work, Isella et al. 2016 derived drops in gas density consistent with Saturn-mass planets inside the gaps in the HD163296 disk through spatially resolved CO isotopologue ob…
We present an observational reconstruction of the radial water vapor content near the surface of the TW Hya transitional protoplanetary disk, and report the first localization of the snow line during this phase of disk evolution. The observations are comprised of Spitzer-IRS, Herschel-PACS, and Herschel-HIFI archival spectra. The abundance structure is retrieved by fitting a two-dimensional disk model to the available star+disk photometry and all observed H2O lines, using a simple step-function parameterization of the water vapor content near the disk surface. We find that water vapor is abund…
Sharp chemical discontinuities can occur in protoplanetary discs, particularly at `snow-lines' where a gas-phase species freezes out to form ice grains. Such sharp discontinuities will diffuse out due to the turbulence suspected to drive angular momentum transport in accretion discs. We demonstrate that the concentration gradient - in the vicinity of the snow-line - of a species present outside a snow-line but destroyed inside is strongly sensitive to the level of turbulent diffusion (provided the chemical and transport time-scales are decoupled) and provides a direct measurement of the radial…
The low water content of the terrestrial planets in the solar system suggests that the protoplanets formed within the water snow line. Accurate prediction of the snow line location moving with time provides a clue to constrain the formation process of the planets. In this paper, we investigate the migration of the snow line in protoplanetary disks whose accretion is controlled by laminar magnetic fields, which have been proposed by various nonideal magnetohydrodynamic (MHD) simulations. We propose an empirical model of the disk temperature based on our nonideal MHD simulations, which show that…
[Abridged] Planet formation is expected to be enhanced around snowlines in protoplanetary disks, in particular around the water snowline. However, the close proximity of the water snowline to the host star and water in the Earth's atmosphere makes a direct detection of the water snowline in protoplanetary disks challenging. Following earlier work on protostellar envelopes, the aim of this research is to investigate the validity of HCO$^+$ and H$^{13}$CO$^+$, as tracers of the water snowline in protoplanetary disks, as HCO$^+$ is destroyed by gas-phase water. Two small chemical networks are use…
Molecular snow lines in protoplanetary disks have been studied theoretically for decades because of their importance in shaping planetary architectures and compositions. The water snow line lies in the planet formation region at < 10 AU, and so far its location has been estimated only indirectly from spatially-unresolved spectroscopy. This work presents a proof-of-concept method to directly image the water snow line in protoplanetary disks through its physical and chemical imprint in the local dust properties. We adopt a physical disk model that includes dust coagulation, fragmentation, drift,…
Planetesimal formation stage represents a major gap in our understanding of the planet formation process. The late-stage planet accretion models typically make arbitrary assumptions about planetesimals and pebbles distribution while the dust evolution models predict that planetesimal formation is only possible at some orbital distances. We want to test the importance of water snow line for triggering formation of the first planetesimals during the gas-rich phase of protoplanetary disk, when cores of giant planets have to form. We connect prescriptions for gas disk evolution, dust growth and fr…
We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of) particles, such as their composition. In this work we focus on the water content of solid particles. Planetesimal formation via streaming instability is taken into account, partly based on previous results on streaming instability outside the water snowline that were presented in Schoonenberg & Ormel (2017). We validate our model by reproducing earlier results from…
Observationally inferred crystalline abundance in silicates in comets, which should have been formed in the outer region of a protoplanetary disk, is relatively high (~ 10-60%), although crystalline silicates would be formed by annealing of amorphous precursors in the disk inner region. In order to quantitatively address this puzzle, we have performed Monte Carlo simulation of advection/diffusion of silicate particles in a turbulent disk, in the setting based on pebble accretion model: pebbles consisting of many small amorphous silicates embedded in icy mantle are formed in the disk outer regi…
Snowlines of major volatiles regulate the gas and solid C/N/O ratios in the planet-forming midplanes of protoplanetary disks. Snow surfaces are the 2D extensions of snowlines in the outer disk regions, where radiative heating results in a decreasing temperature with disk height. CO and N$_2$ are two of the most abundant carriers of C, N and O. N$_2$H$^+$ can be used to probe the snow surfaces of both molecules, because it is destroyed by CO and formed from N$_2$. Here we present Atacama Large Millimeter/submillimeter Array (ALMA) observations of N$_2$H$^+$ at 0.2$''$-0.4$''$ resolution in the …
Current models of (exo)planet formation often rely on a large influx of so-called `pebbles' from the outer disk into the planet formation region. In this paper, we investigate how the formation of pebbles in the cold outer regions of protoplanetary disks and their subsequent migration to the inner disk can alter the gas-phase CO distribution both interior and exterior to the midplane CO snowline. By simulating the resulting CO abundances in the midplane as well as the warm surface layer, we identify observable signatures of large-scale pebble formation and migration that can be used as `smokin…
Highly porous dust aggregates can break through the radial drift barrier, but previous studies assumed disks in their later stage, where the disks have a very small mass and low temperature. In contrast, dust coagulation should begin in the very early stage such as the disk formation stage because the growth timescale of dust is shorter than the disk formation timescale if there is no process to suppress the collisional growth of dust. We investigate the possibility of planetesimal formation via direct collisional growth in the very early stage of a protoplanetary disk. We show that, in the ve…
Context. The water snowline divides dry and icy solid material in protoplanetary disks, and has been thought to significantly affect planet formation at all stages. If dry particles break up more easily than icy ones, then the snowline causes a traffic jam, because small grains drift inward at lower speeds than larger pebbles. Aims. We aim to evaluate the effect of high dust concentrations around the snowline onto the gas dynamics. Methods. Using numerical simulations, we model the global radial evolution of an axisymmetric protoplanetary disk. Our model includes particle growth, evaporation a…
The terrestrial planets and the asteroids dominant in the inner asteroid belt are water poor. However, in the protoplanetary disk the temperature should have decreased below water condensation level well before the disk was photoevaporated. Thus, the global water depletion of the inner Solar System is puzling. We show that, even if the inner disk becomes cold, there cannot be direct condensation of water. This is because the snowline moves towards the Sun more slowly than the gas itself. The appearance of ice in a range of heliocentric distances swept by the snowline can only be due to the rad…
The snowlines of various volatile species in protoplanetary disks are associated with abrupt changes in gas composition and dust physical properties. Volatiles may affect dust growth, as they cover grains with icy mantles that can change the fragmentation velocity of the grains. In turn, dust coagulation, fragmentation, and drift through the gas disk can contribute to the redistribution of volatiles between the ice and gas phases. Here we present the hydrodynamic model FEOSAD for protoplanetary disks with two dust populations and volatile dynamics. We compute the spatial distributions of major…
We investigate dust growth due to settling in a 1D vertical column of a protoplanetary disk. It is known from the observed 10 micron feature in disk SEDs, that small micron-sized grains are present at the disk atmosphere throughout the lifetime of the disk. We hope to explain such questions as what process can keep the disk atmospheres dusty for the lifetime of the disk and how does the particle properties change as a function of height above the midplane. We use a Monte Carlo code to follow the mass and porosity evolution of the particles in time. The used collision model is based on laborato…
We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit de…
Hydrodynamics modeling of the water snow line in young protoplanetary disks with dust-size-dependent opacities
Institut für Astro- und Teilchenphysik, Universität Innsbruck（因斯布鲁克大学天体与粒子物理研究所）；Research Institute of Physics, Southern Federal University（南联邦大学物理研究所）；Institute of Astronomy, Russian Academy of Sciences（俄罗斯科学院天文研究所）
The radial-dependent positions of snowlines of abundant oxygen- and carbon-bearing molecules in protoplanetary discs will result in systematic radial variations in the C/O ratios in the gas and ice. This variation is proposed as a tracer of the formation location of gas-giant planets. However, disc chemistry can affect the C/O ratios in the gas and ice, thus potentially erasing the chemical fingerprint of snowlines in gas-giant atmospheres. We calculate the molecular composition of hot Jupiter atmospheres using elemental abundances extracted from a chemical kinetics model of a disc midplane wh…
Planet formation is thought to begin with the growth of dust particles in protoplanetary disks from micrometer to millimeter and centimeter sizes. Dust growth is hindered by a number of growth barriers, according to dust evolution theory, while observational evidence indicates that somehow these barriers must have been overcome. The observational evidence of dust traps, in particular the Oph IRS 48 disk, with the Atacama Large Millimeter/submillimeter Array (ALMA) has changed our view of the dust growth process. In this article I review the history of dust trapping in models and observations.
Content: For up to a few millions of years, pebbles must provide a quasi-steady inflow of solids from the outer parts of protoplanetary disks to their inner regions. Aims: We wish to understand how a significant fraction of the pebbles grows into planetesimals instead of being lost to the host star. Methods:We examined analytically how the inward flow of pebbles is affected by the snow line and under which conditions dust-rich (rocky) planetesimals form. When calculating the inward drift of solids that is due to gas drag, we included the back-reaction of the gas to the motion of the solids. Re…
The standard model of planet formation considers an initial phase in which planetesimals form from a dust disk, followed by a phase of mutual planetesimal-planetesimal collisions, leading eventually to the formation of planetary embryos. However, there is a potential transition phase (which we call the "snowball phase"), between the formation of the first planetesimals and the onset of mutual collisions amongst them, which has often been either ignored or underestimated in previous studies. In this snowball phase, isolated planetesimals move on Keplerian orbits and grow solely via the direct a…
Pressure maxima are regions in protoplanetary disks where pebbles can be trapped because of the local absence of pressure gradient. These regions could be ideal places to form planetesimals or to isolate isotopic reservoirs. Observations of protoplanetary disks show that dusty rings structures are common, and pressure maxima are sometime invoked as a possible explanation. In our Solar System, pressure bumps have been suggested as a possible mechanism for separating reservoirs with different nucleosynthetic compositions. In this letter we detail a mechanism by which pressure maxima form just in…
We present deep Herschel-PACS spectroscopy of far-infrared water lines from a sample of four protoplanetary disks around solar-mass stars, selected to have strong water emission at mid-infrared wavelengths. By combining the new Herschel spectra with archival Spitzer-IRS spectroscopy, we retrieve a parameterized radial surface water vapor distribution from 0.1-100 AU using two-dimensional dust and line radiative transfer modeling. The surface water distribution is modeled with a step model comprising of a constant inner and outer relative water abundance and a critical radius at which the surfa…
Most protoplanetary discs are thought to undergo violent and frequent accretion outbursts, during which the accretion rate and central luminosity are elevated for several decades. This temporarily increases the disc temperature, leading to the sublimation of ice species as snowlines move outwards. In this paper, we investigate how an FUor-type accretion outburst alters the growth and appearance of dust aggregates at different locations in protoplanetary discs. We develop a model based on the Monte Carlo approach to simulate locally the coagulation and fragmentation of icy dust particles and in…
We investigate the migration of a low-mass ($\lesssim 10 M_\oplus$) planet near the inner edge of a protoplanetary disc using two-dimensional viscous hydrodynamics simulations. We employ an inner boundary condition representing the truncation of the disc at the stellar corotation radius. As described by Tsang (2011), wave reflection at the inner disc boundary modifies the Type I migration torque on the planet, allowing migration to be halted before the planet reaches the inner edge of the disc. For low-viscosity discs ($α\lesssim 10^{-3}$), planets may be trapped with semi-major axes as large …
The processes that govern the evolution of dust and water (in the form of vapor or ice) in protoplanetary disks are intimately connected. We have developed a model that simulates dust coagulation, dust dynamics (settling, turbulent mixing), vapor diffusion, and condensation/sublimation of volatiles onto grains in a vertical column of a protoplanetary disk. We employ the model to study how dust growth and dynamics influence the vertical distribution of water vapor and water ice in the region just outside the radial snowline. Our main finding is that coagulation (boosted by the enhanced stickine…
A snow-line is the region of a protoplanetary disk at which a major volatile, such as water or carbon monoxide, reaches its condensation temperature. Snow-lines play a crucial role in disk evolution by promoting the rapid growth of ice-covered grains. Signatures of the carbon monoxide snow-line (at temperatures of around 20 kelvin) have recently been imaged in the disks surrounding the pre-main-sequence stars TW Hydra and HD163296, at distances of about 30 astronomical units (au) from the star. But the water snow-line of a protoplanetary disk (at temperatures of more than 100 kelvin) has not h…
ALMA has revolutionized our view of protoplanetary disks, revealing structures such as gaps, rings and asymmetries that indicate dust trapping as an important mechanism in the planet formation process. However, the high resolution images have also shown that the optically thin assumption for millimeter continuum emission may not be valid and the low values of the spectral index may be related to optical depth rather than dust growth. Longer wavelength observations are essential to properly disentangle these effects. The high sensitivity and spatial resolution of the next-generation Very Large …
Since the discovery of the multi-ring structure of the HL Tau disk, ALMA data suggest that the dust continuum emission of many, if not all, protoplanetary disks consists of rings and gaps, no matter their spectral type or age. The origin of these gaps so far remains unclear. We present a sample study of 16 disks with multiple ring-like structures in the continuum, using published ALMA archival data, to compare their morphologies and gap locations in a systematic way. The 16 targets range from early to late type stars, from <0.5 Myr to >10 Myr, from ~0.2 to 40 L_Sun and include both full and tr…
We study dust concentration in axisymmetric gas rings in protoplanetary disks. Given the gas surface density, we derived an analytical total dust surface density by taking into account the differential concentration of all the grain sizes. This model allows us to predict the local dust-to-gas mass ratio and the slope of the particle size distribution, as a function of radius. We test this analytical model comparing it with a 3D magneto-hydrodynamical simulation of dust evolution in an accretion disk. The model is also applied to the disk around HD 169142. By fitting the disk continuum observat…
In protoplanetary disks, the differential gravity-driven settling of dust grains with respect to gas and with respect to grains of varying sizes determines the observability of grains, and sets the conditions for grain growth and eventually planet formation. In this work we explore the effect of photophoresis on the settling of large dust grains in the inner regions of actively accreting protoplanetary disks. Photophoretic forces on dust grains result from the collision of gas molecules with differentially heated grains. We undertake one dimensional dust settling calculations to determine the …
In this paper, we analyse the upper limit fluxes of sub-millimeter ortho-H$_{2}$$^{16}$O 321 GHz, para-H$_{2}$$^{18}$O 322 GHz, and HDO 335 GHz lines from the protoplanetary disk around the Herbig Ae star HD 163296, using the Atacama Large Millimeter/Submillimeter Array (ALMA). These water lines are considered to be the best candidate sub-millimeter lines to locate the position of the H$_{2}$O snowline, on the basis of our previous model calculations. We compare the upper limit fluxes with the values calculated by our models with dust emission included, and we constrain the line emitting regio…
Planet traps are necessary to prevent forming planets from falling onto their host star by type I migration. Surface mass density and temperature gradient irregularities favor the apparition of traps and deserts. Such features are found at the dust sublimation lines and heat transition barriers. We study how planets may remain trapped or escape as they grow and as the disk evolves. We model the temporal viscous evolution of a protoplanetary disk by coupling its dynamics, thermodynamics, geometry and composition. The resulting mid-plane density and temperature profiles allow the modeling of the…
Volatile species in protoplanetary discs can undergo a phase change from vapour to solid. These "snow-lines" can play vital roles in planet formation at all scales, from dust coagulation to planetary migration. In the outer regions of protoplanetary discs, the temperature profile is set by the absorption of reprocessed stellar light by the solids. Further, the temperature profile sets the distribution of solids through sublimation and condensation at various snow-lines. Hence the snow-line position depends on the temperature profile and vice-versa. We show that this coupling can be thermally u…
Dust plays a key role in the formation of planets and its emission also provides one of our most accessible views of protoplanetary discs. If set by radiative equilibrium with the central star, the temperature of dust in the disc plateaus at around $10-20$K in the outer regions. However sufficiently nearby massive stars can heat the outer disc to substantially higher temperatures. In this paper we study the radiative equilibrium temperature of discs in the presence of massive external sources and gauge the effect that it has on millimetre dust mass estimates. Since millimetre grains are not en…
In most theories of planet formation, the snow-line represents a boundary between the emergence of the interior rocky planets and the exterior ice giants. The wide separation of the snow-line makes the discovery of transiting worlds challenging, yet transits would allow for detailed subsequent characterization. We present the discovery of Kepler-421b, a Uranus-sized exoplanet transiting a G9/K0 dwarf once every 704.2 days in a near-circular orbit. Using public Kepler photometry, we demonstrate that the two observed transits can be uniquely attributed to the 704.2 day period. Detailed light cur…
The question of what determines the width of Kuiper belt analogues (exoKuiper belts) is an open one. If solved, this understanding would provide valuable insights into the architecture, dynamics, and formation of exoplanetary systems. Recent observations by ALMA have revealed an apparent paradox in this field, the presence of radially narrow belts in protoplanetary discs that are likely the birthplaces of planetesimals, and exoKuiper belts nearly four times as wide in mature systems. If the parent planetesimals of this type of debris disc indeed form in these narrow protoplanetary rings via st…
While giant planet occurrence rates increase with stellar mass, occurrence rates of close-in super-Earths decrease. This is in contradiction to the expectation that the total mass of the planets in a system scale with the protoplanetary disc mass and hence the stellar mass. Since the snow line plays an important role in the planet formation process we examine differences in the temperature structure of protoplanetary gas discs around stars of different mass. Protoplanetary discs likely contain a dead zone at the midplane that is sufficiently cold and dense for the magneto-rotational instabilit…
